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Paper Abstract and Keywords
Presentation 2012-12-10 15:15
A Lower Bound of Minimum Energy Broadcast on Two Dimensional Triangular Grid Wireless Networks
Youhei Kouchi, Akira Matsubayashi (Kanazawa Univ.) COMP2012-48
Abstract (in Japanese) (See Japanese page) 
(in English) The minimum energy broadcast problem is to assign a transmission range to each node in an ad hoc wireless network to construct a spanning tree rooted at a given source node such that any non-root node resides within the transmission range of its parent. The objective is to minimize the total energy consumption, i.e., the sum of the $\delta$th powers of a transmission range ($\delta\geq1$). In this report, we consider the case that $\delta=2$, and that $n=kl$ nodes are located on a 2-dimensional triangular grid with $l$ columns at an angle of 60 degrees to $k\leq l$ rows. We prove that the minimum energy consumption for the $n$-node $k\times l$-triangular grid is at least $\frac{\sqrt{3}n}{2\pi}+\Omega(\frac{n}{k})-O(k)$. Our lower bound closes the previous gap of upper and lower bounds for triangular grids. This lower bound is consistent with the known upper bound $\frac{\sqrt{3}n}{2\pi}+O(\frac{n}{k^{0.68}})$ within an $o(n)$ term as long as $k=\omega(1)$.
Keyword (in Japanese) (See Japanese page) 
(in English) energy minimization / broadcast / triangular grid / ad hoc wireless network / / / /  
Reference Info. IEICE Tech. Rep., vol. 112, no. 340, COMP2012-48, pp. 27-31, Dec. 2012.
Paper # COMP2012-48 
Date of Issue 2012-12-03 (COMP) 
ISSN Print edition: ISSN 0913-5685    Online edition: ISSN 2432-6380
Copyright
and
reproduction		 All rights are reserved and no part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopy, recording, or any information storage and retrieval system, without permission in writing from the publisher. Notwithstanding, instructors are permitted to photocopy isolated articles for noncommercial classroom use without fee. (License No.: 10GA0019/12GB0052/13GB0056/17GB0034/18GB0034)
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Conference Information
Committee COMP  
Conference Date 2012-12-10 - 2012-12-10 
Place (in Japanese) (See Japanese page) 
Place (in English) Kyushu University 
Topics (in Japanese) (See Japanese page) 
Topics (in English)  
Paper Information
Registration To COMP 
Conference Code 2012-12-COMP 
Language Japanese 
Title (in Japanese) (See Japanese page) 
Sub Title (in Japanese) (See Japanese page) 
Title (in English) A Lower Bound of Minimum Energy Broadcast on Two Dimensional Triangular Grid Wireless Networks 
Sub Title (in English)  
Keyword(1) energy minimization  
Keyword(2) broadcast  
Keyword(3) triangular grid  
Keyword(4) ad hoc wireless network  
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1st Author's Name Youhei Kouchi  
1st Author's Affiliation Kanazawa University (Kanazawa Univ.)
2nd Author's Name Akira Matsubayashi  
2nd Author's Affiliation Kanazawa University (Kanazawa Univ.)
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Speaker Author-1 
Date Time 2012-12-10 15:15:00 
Presentation Time 35 minutes 
Registration for COMP 
Paper # COMP2012-48 
Volume (vol) vol.112 
Number (no) no.340 
Page pp.27-31 
#Pages 5 
Date of Issue 2012-12-03 (COMP) 

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